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June 2004 G-Norm Properties of Bounded Variation Regularization
Stanley Osher, Otmar Scherzer
Commun. Math. Sci. 2(2): 237-254 (June 2004).


Recently Y. Meyer derived a characterization of the minimizer of the Rudin-Osher-Fatemi functional in a functional analytical framework. In statistics the discrete version of this functional is used to analyze one dimensional data and belongs to the class of nonparametric regression models. In this work we generalize the functional analytical results of Meyer and apply them to a class of regression models, such as quantile, robust, logistic regression, for the analysis of multidimensional data. The characterization of Y. Meyer and our generalization is based on G-norm properties of the data and the minimizer. A geometric point of view of regression minimization is provided.


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Stanley Osher. Otmar Scherzer. "G-Norm Properties of Bounded Variation Regularization." Commun. Math. Sci. 2 (2) 237 - 254, June 2004.


Published: June 2004
First available in Project Euclid: 1 March 2005

zbMATH: 1082.49003
MathSciNet: MR2119940

Rights: Copyright © 2004 International Press of Boston

Vol.2 • No. 2 • June 2004
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